(Strange Universe Series) How can order emerge out of chaos?

Right after the Big Bang, the Universe was almost infinitely hot and energetic. It was so energetic that even the most basic particles such as atoms could not coalesce out of the seething, frothing sea of sub-atomic chaos. And yet somehow out of all this disorder, instead of entropy ruling and the disorder just spreading and cooling, order arose. Atoms formed, then molecules. Gas clouds drifted closer and closer together. Stars formed, stars clustered into well-organized galaxies.

Even today, we see examples of order emerging from chaos all around us. The symmetry of patterns the chaotic desert winds form in sand dunes and the meandering of rivers. All sorts of patterns emerge in nature from completely stochastic processes. We see the same thing mirrored in certain chemical reactions and behavior of materials when pushed far from equilibrium. See Benard-Marangoni convection, a Complex Ginzburg-Landau Reaction-Diffusion, a Belousov-Zhabotinsky reaction, and a Briggs-Rauscher Oscillating Reaction.

What other examples of self organization can you think of where apparent chaos produces emergent order? Please feel free to post links to photos or videos showing the process. Why do complex, organized structures similar to Mandlebrot Sets and Fractals appear everywhere in nature? What implications can you see in order arising from chaos?

This is a continuation in the Strange Universe series.
1—Where is the center of the Universe?
2—If CERN proves there are parallel universes, will you move?
3—If the universe expands at faster than the speed of light, does it begin to go back in time?
4—What is the expanding universe expanding into?
5—Big Bang Theory—How can you divide infinity into a single finite whole?
6—How would you answer this speed-of-light question?
7—What happens when the expansion of the Universe reaches the speed of light?
8—What’s your Strange Universe example to illustrate Sir Arthur Eddington’s quote?